Randomized Algorithms

CS388R: Randomized Algorithms (Fall 2019)

Logistics:	Tue/Thu 3:30 - 5:00 GDC 4.302 Course web page: http://www.cs.utexas.edu/~ecprice/courses/randomized/
Professor:	Eric Price Email: `ecprice@cs.utexas.edu` Office: GDC 4.510 Office Hours: 5-6pm Tuesday
TA: Akshay Kamath	Office Hours: Thursday, 12-1 and 5-6 in GDC basement.
Useful References:	Previous offerings (2015, 2017) have relevant information. Similar courses are offered at MIT and Berkeley.
Problem Sets:	Problem Set 1 (tex), due Thursday, September 5. Problem Set 2 (tex), due Thursday, September 12. Problem Set 3 (tex), due Friday, September 20. Problem Set 4 (tex), due Friday, September 27. Problem Set 5 (tex), due Friday, October 4. Problem Set 6 (tex), due Friday, October 11. Problem Set 7 (tex), due Friday, October 18. Problem Set 8 (tex), due Friday, October 25. Problem Set 9 (tex), due Friday, November 8. Problem Set 10 (tex), due Friday, November 15. Problem Set 11 (tex), due Friday, November 22.
Lecture Notes:	August 29th, Lecture notes 1 (source): Introduction to randomized algorithms; min-cut. September 1, Lecture notes 2 (source): Concentration inequalities. September 10, Lecture notes 4 (source): Von Neumann's theorem, Yao's principle. September 12, Lecture notes 5 (source): Coupon Collector; Balls and Bins. September 17, Lecture notes 6 (source): Power of Two Choices. September 19, Lecture notes 7 (source): Probability Puzzles. September 24th, Lecture notes 8 (source): Cuckoo Hashing. September 26th, Lecture notes 9 (source): Limited Independence. October 1, Lecture notes 10 (source): Routing. October 3, Lecture notes 11 (source): Fingerprinting. October 8th, Lecture notes 12 (source): All Pairs Shortest Path. October 10, Lecture notes 13 (source): Bipartite Matching on regular graphs. October 15th, Lecture notes 14 (source): Online Bipartite Matching. October 17, Lecture notes 15 (source): K-Hamiltonian Path; Sampling; median finding;. October 22nd, Lecture notes 16 (source): Concentration Inequalities. October 24th, Lecture notes 17 (source): Subgamma variables and Johnson-Lindenstrauss. Oct. 31, Lecture notes 19 (source): Streaming (continued). Nov. 5, Lecture notes 20 (source): Bloom Filters. November 7th, Lecture notes 21 (source): Matrix concentration and Graph Sparsification. November 12th, Lecture notes 22 (source): Spectral Sparsification. November 14th, Lecture notes 23 (source): Network Coding \& Edge Connectivity. November 19th, Lecture notes 24 (source): Markov Chains. November 21, Lecture notes 25 (source): Random Walk on Undirected Graphs; Closest Pair in Plane. November 26, Lecture notes 26 (source): Computational Geometry. December 3rd, Lecture notes 27 (source): Review. December 5th, Lecture notes 28 (source): Locality Sensitive Hashing.
Content:	This graduate course will study the use of randomness in algorithms. Over the past thirty years, randomization has become an increasingly important part of theoretical computer science. The tentative outline for the course is as follows: Basic probability; the minimax principle; limited independence More advanced concentration of measure: subgaussian and subgamma variables Balls in bins; negatively associated random variables Hashing: universal, perfect, cuckoo Fingerprinting; Bloom filters Network coding; edge connectivity Graph sparsification Parallel algorithms; symmetry breaking Randomized approximation algorithms Streaming algorithms Stochastic gradient descent; SVRG Random walks: cover times, markov chains, mixing rates.
Prerequisites:	Mathematical maturity and comfort with undergraduate algorithms and basic probability.
Grading:	40%: Homework 20%: Final exam 20%: Midterm exam 20%: Scribing lectures
Scribing:	In each class, two students will be assigned to take notes. These notes should be written up in a standard LaTeX format before the next class.
Text:	You may find the text Randomized Algorithms by Motwani and Raghavan to be useful, but it is not required.
Homework policy:	There will be a homework assignment every 1-2 weeks. Collaboration policy: You are encouraged to collaborate on homework. However, you must write up your own solutions. You should also state the names of those you collaborated with on the first page of your submission.
Students with Disabilites:	Any student with a documented disability (physical or cognitive) who requires academic accommodations should contact the Services for Students with Disabilities area of the Office of the Dean of Students at 471-6259 (voice) or 471-4641 (TTY for users who are deaf or hard of hearing) as soon as possible to request an official letter outlining authorized accommodations.